King-plot analysis of isotope shifts in simple diatomic molecules

We demonstrate that the isotope shift in isotopomers of diatomic molecules, where the nucleus of one of its constituent atoms is replaced by another isotope, can be expressed as the sum of a field shift and a mass shift, similar to the atomic case. We show that a linear relation holds between atomic and molecular isotopes shifts, thus extending the King-plot analysis to molecular isotope shifts. Optical isotope shifts in YbF and ZrO and infrared isotope shifts in SnH are analyzed with a molecular King-plot approach, utilizing Yb$^{+}$ and Zr$^{+}$ ionic isotope shifts and charge radii of Sn obtained with non-optical methods. The changes in the mean-squared nuclear charge radii $\delta \langle r^2 \rangle$ of $^{170-174,176}$Yb and $^{90-92,94,96}$Zr extracted from the molecular transitions are found to be in excellent agreement with the values from the spectroscopy of Yb$^{+}$ and Zr$^{+}$, respectively. On the contrary, in the case of the vibrational-rotational transition in SnH, no sensitivity to the nuclear volume could be deduced within the experimental resolution, which makes it unsuitable for the extraction of nuclear charge radii but provides insights into the molecular electronic wave function not accessible via other methods. The new opportunities offered by the molecular King-plot analysis for research in nuclear structure and molecular physics are discussed.Comment: Accepted at Physical Review X. Link to abstract: https://journals.aps.org/prx/accepted/be075Kf7E0c16505459d9fa833408356a593fd90

Nuclear Charge Radius of 12^{12}Be

The nuclear charge radius of $^{12}$Be was precisely determined using the technique of collinear laser spectroscopy on the $2s_{1/2}\rightarrow 2p_{1/2, 3/2}$ transition in the Be$^{+}$ ion. The mean square charge radius increases from $^{10}$Be to $^{12}$Be by \delta ^{10,12} = 0.69(5) \fm^{2} compared to \delta ^{10,11} = 0.49(5) \fm^{2} for the one-neutron halo isotope $^{11}$Be. Calculations in the fermionic molecular dynamics approach show a strong sensitivity of the charge radius to the structure of $^{12}$Be. The experimental charge radius is consistent with a breakdown of the N=8 shell closure.Comment: 5 pages, 3 figure

Collinear laser spectroscopy of atomic cadmium

Hyperfine structure $A$ and $B$ factors of the atomic 5s\,5p\,\; ^3\rm{P}_2 \rightarrow 5s\,6s\,\; ^3\rm{S}_1 transition are determined from collinear laser spectroscopy data of $^{107-123}$Cd and $^{111m-123m}$Cd. Nuclear magnetic moments and electric quadrupole moments are extracted using reference dipole moments and calculated electric field gradients, respectively. The hyperfine structure anomaly for isotopes with $s_{1/2}$ and $d_{5/2}$ nuclear ground states and isomeric $h_{11/2}$ states is evaluated and a linear relationship is observed for all nuclear states except $s_{1/2}$. This corresponds to the Moskowitz-Lombardi rule that was established in the mercury region of the nuclear chart but in the case of cadmium the slope is distinctively smaller than for mercury. In total four atomic and ionic levels were analyzed and all of them exhibit a similar behaviour. The electric field gradient for the atomic 5s\,5p\,\; ^3\mathrm{P}_2 level is derived from multi-configuration Dirac-Hartree-Fock calculations in order to evaluate the spectroscopic nuclear quadrupole moments. The results are consistent with those obtained in an ionic transition and based on a similar calculation.Comment: 12 pages, 5 figure

Precision Test of Many-Body QED in the Be+^+ 2p2p Fine Structure Doublet Using Short-Lived Isotopes

Absolute transition frequencies of the 2s\; ^2{\rm S}_{1/2} \rightarrow 2p\;^2\mathrm{P}_{1/2,3/2} transitions in Be$^+$ were measured for the isotopes $^{7,9-12}$Be. The fine structure splitting of the $2p$ state and its isotope dependence are extracted and compared to results of \textit{ab initio} calculations using explicitly correlated basis functions, including relativistic and quantum electrodynamics effects at the order of $m \alpha^6$ and $m \alpha^7 \ln \alpha$. Accuracy has been improved in both the theory and experiment by 2 orders of magnitude, and good agreement is observed. This represents one of the most accurate tests of quantum electrodynamics for many-electron systems, being insensitive to nuclear uncertainties.Comment: 5 pages, 2 figure

Voltage scanning and technical upgrades at the Collinear Resonance Ionization Spectroscopy experiment

To optimize the performance of the Collinear Resonance Ionization Spectroscopy (CRIS) experiment at CERN-ISOLDE, technical upgrades are continuously introduced, aiming to enhance its sensitivity, precision, stability, and efficiency. Recently, a voltage-scanning setup was developed and commissioned at CRIS, which improved the scanning speed by a factor of three as compared to the current laser-frequency scanning approach. This leads to faster measurements of the hyperfine structure for systems with high yields (more than a few thousand ions per second). Additionally, several beamline sections have been redesigned and manufactured, including a new field-ionization unit, a sharper electrostatic bend, and improved ion optics. The beamline upgrades are expected to yield an improvement of at least a factor of 5 in the signal-to-noise ratio by suppressing the non-resonant laser ions and providing time-of-flight separation between the resonant ions and the collisional background. Overall, the presented developments will further improve the selectivity, sensitivity, and efficiency of the CRIS technique.Comment: 10 pages. Under review at NIM B as part of the proceedings of EMIS 2022 at RAON, South Kore

The nuclear magnetic moment of ²⁰⁸Bi and its relevance for a test of bound-state strong-field QED

The hyperfine structure splitting in the 6p2 4S3/2 -> 6p27s 4P1/2 transition at 307 nm in atomic 208Bi was measured with collinear laser spectroscopy at ISOLDE, CERN. The hyperfine A and B factors of both states were determined with an order of magnitude improved accuracy. Based on these measurements, theoretical input for the hyperfine structure anomaly, and results from hyperfine measurements on hydrogen-like and lithium-like 209Bi80+,82+, the nuclear magnetic moment of 208Bi has been determined to μ(208Bi) =+4.570(10) μN . Using this value, the transition energy of the ground-state hyperfine splitting in hydrogen-like and lithium-like 208Bi80+,82+ and their specific difference of −67.491(5)(148) meV are predicted. This provides a means for an experimental confirmation of the cancellation of nuclear structure effects in the specific difference in order to exclude such contributions as the cause of the hyperfine puzzle, the recently reported 7-σ discrepancy between experiment and bound-state strong-field QED calculations of the specific difference in the hyperfine structure splitting of 209Bi80+,82+

Nuclear charge radii of potassium isotopes beyond N = 28

We report on the measurement of optical isotope shifts for ³⁸, ³⁹, ⁴², ⁴⁴, ⁴⁶⁻⁵¹K relative to ⁴⁷K from which changes in the nuclear mean square charge radii across the N = 28 shell closure are deduced. The investigation was carried out by bunched-beam collinear laser spectroscopy at the CERN-ISOLDE radioactive ion-beam facility. Mean square charge radii are now known from ³⁷K to ⁵¹K, covering all ν f₇/₂-shell as well as all ν p₃/₂-shell nuclei. These measurements, in conjunction with those of Ca, Cr, Mn and Fe, provide a first insight into the Z dependence of the evolution of nuclear size above the shell closure at N = 28

Structural trends in atomic nuclei from laser spectroscopy of tin

Tin is the chemical element with the largest number of stable isotopes. Its complete proton shell, comparable with the closed electron shells in the chemically inert noble gases, is not a mere precursor to extended stability; since the protons carry the nuclear charge, their spatial arrangement also drives the nuclear electromagnetism. We report high-precision measurements of the electromagnetic moments and isomeric differences in charge radii between the lowest 1/2(+), 3/2(+), and 11/2(-) states in Sn117-131, obtained by collinear laser spectroscopy. Supported by state-of-the-art atomic-structure calculations, the data accurately show a considerable attenuation of the quadrupole moments in the closed-shell tin isotopes relative to those of cadmium, with two protons less. Linear and quadratic mass-dependent trends are observed. While microscopic density functional theory explains the global behaviour of the measured quantities, interpretation of the local patterns demands higher-fidelity modelling. Measurements of the hyperfine structure of chemical elements isotopes provide unique insight into the atomic nucleus in a nuclear model-independent way. The authors present collinear laser spectroscopy data obtained at the CERN ISOLDE and measure hyperfine splitting along a long chain of odd-mass tin isotopes.Peer reviewe

Quadrupole moments of odd-A ⁵³⁻⁶³Mn: Onset of collectivity towards N = 40

The spectroscopic quadrupole moments of the odd–even Mn isotopes between N=28 and N=38 have been measured using bunched-beam collinear laser spectroscopy at ISOLDE, CERN. In order to increase sensitivity to the quadrupole interaction, the measurements have been done using a transition in the ion rather than in the atom, with the additional advantage of better spectroscopic efficiency. Since the chosen transition is from a metastable state, optical pumping in ISOLDE’s cooler and buncher (ISCOOL) was used to populate this state. The extracted quadrupole moments are compared to large-scale shell model predictions using three effective interactions, GXPF1A, LNPS and modified A3DA. The inclusion of both the 1νg9/2and 2νd5/2orbitals in the model space is shown to be necessary to reproduce the observed increase in the quadrupole deformation from N=36 onwards. Specifically, the inclusion of the 2νd5/2orbital induces an increase in neutron and proton excitations across the reduced gaps at N=40and Z=28, leading to an increase in deformation above N=36

Nuclear charge radii of ⁶²⁻⁸⁰Zn and their dependence on cross-shell proton excitations

Nuclear charge radii of ⁶²⁻⁸⁰Zn have been determined using collinear laser spectroscopy of bunched ion beams at CERN-ISOLDE. The subtle variations of observed charge radii, both within one isotope and along the full range of neutron numbers, are found to be well described in terms of the proton excitations across the Z = 28 shell gap, as predicted by large-scale shell model calculations. It comprehensively explains the changes in isomer-to-ground state mean square charge radii of ⁶⁹⁻⁷⁹Zn, the inversion of the odd-even staggering around N = 40 and the odd-even staggering systematics of the Zn charge radii. With two protons above Z = 28, the observed charge radii of the Zn isotopic chain show a cumulative effect of different aspects of nuclear structure including single particle structure, shell closure, correlations and deformations near the proposed doubly magic nuclei, ⁶⁸Ni and ⁷⁸Ni